Title (CMMSE paper) Algorithm to compute minimal matrix representation of nilpotent lie algebras
Authors CEBALLOS GONZÁLEZ, MANUEL, Núñez J. , Tenorio Á.F.
External publication No
Scope Article
Nature Científica
JCR Quartile 2
SJR Quartile 2
JCR Impact 1.6
SJR Impact 0.548
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85062340347&doi=10.1080%2f00207160.2018.1557639&partnerID=40&md5=06570ba149744b3683fc5c127c7be357
Publication date 27/02/2019
ISI 000505888300020
Scopus Id 2-s2.0-85062340347
DOI 10.1080/00207160.2018.1557639
Abstract As it is well-known there exist matrix representations of any given finite-dimensional complex Lie algebra. More concretely, such representations can be obtained by means of an isomorphic matrix Lie algebra consisting of upper-triangular square matrices. However, there is no general information about the minimal order for the matrices involved in such representations. In this way, our main goal is to revisit, debug and implement an algorithm which provides the minimal order for matrix representations of any finite-dimensional nilpotent Lie algebra from its law, as well as returning a matrix representative of such an algebra by using the minimal order previously computed. In order to show the applicability of this procedure, we have computed minimal representative for each nilpotent Lie algebra of dimensions 6 and 7 and we have also obtained the representation of some families with an arbitrary dimension. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.
Keywords Program debugging; Matrix representation; Minimal representation; Nilpotent lie algebras; Numerical algorithms; Symbolic computation; Matrix algebra
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